a-conjecture-of-mine

 // The following program is a simple test for the following conjecture:
 
 // Let S: N -> N be the sum of the digits of a positive integer.
 // For all A and B in N, S(A + B) = S(A) + S(B) - 9k, where k is an integer.
 
 import java.util.InputMismatchException;
 
 public class Main {
     private static final int SUCCESS = 0;
     private static final int FAIL = 1;
     private static final int INVALID_INPUT = 2;
 
     public static void main(String[] args) {
         try {
             int max = Integer.parseInt(args[0]);
             if (max <= 0) throw new IllegalArgumentException();
 
             if (counterexample(max)) {
                 System.exit(FAIL);
             } else {
                 System.exit(SUCCESS);
             }
         } catch (Exception error) {
             System.exit(INVALID_INPUT);
         }
 
     }
 
     private static Boolean counterexample(int max) {
         int[] sum = getSums(max);
 
         for (int a = 0; a <= max; a++)
             for (int b = a; b <= max; b++) {
                 int diff = sum[a + b] - sum[a] - sum[b];
 
                 if (diff % 9 != 0)
                     return true;
             }
 
         return false;
     }
 
     private static int[] getSums(int max) {
         int maxRange = 2 * max + 1;
         int[] sums = new int[maxRange];
 
         for (int i = 0; i < maxRange; i++)
             sums[i] = sumDigits(i);
 
         return sums;
     }
 
     /**
      * Calculates the sum of the digits of a positive integer.
      */
     private static int sumDigits(int n) {
         int num = n, sum = 0;
 
         while (num > 0) {
             sum += num % 10;
             num /= 10;
         }
 
         return sum;
     }
 }